ArcGIS Pro 3.2.1
Background regarding join tools:
The two tools have similar names but seem to have different implementations. Add Join produces a dynamic/temporary join, whereas Add Spatial Join outputs a static FC to the project's scratch.gdb.
With Add Spatial Join, if I were to edit the features (such as move features so that they no longer intersect), the join wouldn't reflect those changes; the spatial join is static and so it would become out of date.
Idea:
You wouldn't know that the Add Spatial Join tool outputs a static FC when looking at the tool or by reading the docs. Could Add Spatial Join be enhanced so that there is an indication in the tool that a static FC is created? Or let the user specify where the FC will be saved?
I'm aware that the Add Spatial Join tool utilizes a non-spatial join to link the target features to the spatial join FC (from scratch.gdb). That makes sense, but maybe isn't relevant to this idea.